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《Ordnance Material Science and Engineering》 2004-02
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Application of multi-fractal on diagnosis of smart materials and structures

YANG Ming, LIANG Da-kai, WAN Peng-fei (Aeronautical Science Key Laboratory for Smart Materials and Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China)  
The implication of multi-fractal spectrum is more profound with profusion of information than the simply fractal dimension. In settling the engineering-oriented problems, the multi-fractal spectrum is mainly to describe the random probability distribution of physical phenomenon. Before the damage of structures occurrence, the multi-fractal spectrum of space distribution of interior strain changes from centralized to loose, which indicates that complexity of damage fractal structure and the inhomogeneity of space distribution are both increasing. By studying the numerical simulation of point sets, the conclusion is drawn that the physical essence of multi-fractal spectrums before and after the damage of smart materials and structures occurrence is a ever-changing process from homogeneous to inhomogeneous, from simple to complex. The calculated result upon the data of a specimen, into which fiber sensors network is embedded and its size is 5×5 (units), indicates that the diagnosis method is reliable and practical.
【Fund】: 国家自然科学基金 ( 5 0 13 5 0 3 0 )资助项目
【CateGory Index】: TB381
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